¹Anadolu University, Faculty of Science, Department of Statistics, Eskisehir, Turkey. Professor. Email: sacitas@anadolu.edu.tr
²Ankara University, Faculty of Science, Department of Statistics, Ankara, Turkey. Professor. Email: senoglu@science.ankara.edu.tr
³Ankara University, Faculty of Science, Department of Statistics, Ankara, Turkey. Professor. Email: oarslan@ankara.edu.tr

The alpha-skew normal (ASN) distribution has been proposed recently in the literature by using standard normal distribution and a skewing approach. Although ASN distribution is able to model both skew and bimodal data, it is shortcoming when data has thinner or thicker tails than normal. Therefore, we propose an alpha-skew generalized t (ASGT) by using the generalized t (GT) distribution and a new skewing procedure. From this point of view, ASGT can be seen as an alternative skew version of GT distribution. However, ASGT differs from the previous skew versions of GT distribution since it is able to model bimodal data sest as well as it nests most commonly used density functions. In this paper, moments and maximum likelihood estimation of the parameters of ASGT distribution are given. Skewness and kurtosis measures are derived based on the first four noncentral moments. The cumulative distribution function (cdf) of ASGT distribution is also obtained. In the application part of the study, two real life problems taken from the literature are modeled by using ASGT distribution.

Key words: Bimodality, Kurtosis, Maximum Likelihood Estimation, Modeling, Skewness.

La distribución normal alfa-sesgada (ASN por sus siglas en inglés) ha sido propuesta recientemente en la literatura mediante el uso de una distribución normal estándar y procedimientos de sesgo. Aunque la distribución ASN es capaz de modelar tanto datos sesgados y bimodales, no es recomendada cuando los datos tienen colas más livianas o pesadas que la distribución normal. Por lo tanto, se propone una distribución t alfa-sesgada generalizada (ASGT por sus siglas en inglés) mediante el uso de la distribución t generalizada (GT por sus siglas en inglés) y un nuevo procedimiento de sesgo. Bajo este punto de vista, la distribución ASGT se puede ver como una alternativa sesgada de la distribución GT. Sin embargo, ASGT difiere de previas versiones sesgadas de la distribución GT puesto que es capaz de modelar datos bimodales y agrupa funciones de densidad más comúnmente usadas. En este artículo, los momentos y la estimación máximo verosímil de los parámetros de la distribución ASGT son derivadas. Medidas del sesgo y la curtosis son derivadas con base a los primeros cuatro momentos no centrales. La función de distribución acumulada (cdf por sus siglas en inglés) de la distribución ASGT es también obtenida. En la parte de aplicación del estudio, dos problemas reales tomados de la literatura son modelados usando la distribución ASGT.

Palabras clave: bimodalidad, curtosis, estimación máximo verosímil, \linebreak modelamiento, sesgo.

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